The little dancing black spots that you see are called floaters. They are normally proteins that have just clumped together in the fluid. These clumps casts shadows on the retina (the part of your eye that responds to light). Here’s a good article on the NHS about them: http://www.nhs.uk/conditions/floaters/Pages/Introduction.aspx
So the shadows that you see are usually clumps of proteins that have formed inside your eyeball.
Another interesting fact about your eye is that the part of the eye that sends the information about what you’re seeing to the brain (called the optic nerve) is connected at the retina (the light sensitive part). It’s like having to plug the power cable for a TV directly into the screen. It creates a dark spot. So if we just look out of one eye, then there will be things that we can’t see. We call this the blind spot. This website tells you how you can find your blind spot if you scroll down to the paragraph below the spot and the cross: http://io9.com/5804116/why-every-human-has-a-blind-spot—and-how-to-find-yours
Whilst the black spots aren’t normally a cause for concern, if you get loads of them all of a sudden, like a shower, it could mean you have a serious problem that lead to eye detachment. Thankfully this is pretty rare, but worth being aware of!